Flux is a central concept in electromagnetism. For a small surface it is the product of the normal component of B and the surface element (B.dS). For a larger surface it is the integral of this product over the whole surface. The Maxwell equation ∇.B = 0 can be interpreted via a very useful theorem of Gauss to imply that the magnetic flux though any closed surface is zero. This says that there are no sources of magnetic field that are analogous to electric charges. Currents produce magnetic fields but fields that always both emerge and return so that the flux through any closed surface is zero even if it contains a current within it.

Changing magnetic flux through a circuit generates an EMF in the circuit, which is what Faraday discovered. This is the effect underlying dynamos and alternators that produce voltage and current from mechanical work. The electrical generator mechanism creates motion of magnetic flux through a circuit by moving the magnetic field or the circuit, or both. Nuclear power stations, wind, tidal and biogas electric generators and conventional power stations all use this effect. Without it we would be left with little except solar panels to charge our batteries.

JSR 2016